element

The element command is used to construct finite elements. Please refer to the specific type of elements for syntax and details.

General Syntax

In general, the syntax uses the following pattern:

element <name> <tag> <connected_nodes> <associated_material> <other_specific_parameters>

Output Types

All elements support record elemental stiffness and mass by tokens K and M. One can use the following to record them. The detailed syntax can be seen in Record page.

hdf5recorder (1) Element K (2...)
hdf5recorder (1) Element M (2...)
# (1) int, unique recorder tag
# (2...) int, element tags that K or M needs to be recorded

The matrices are vectorised.

Most elements do not support additional quantities to be recorded. There are some exceptions, however. The additional ones will be documented in the specific element documentation.

The recording command will be directly forwarded to the attached material models. Take the CP4 element for instance, it uses a second order Gaussian quadrature, that is four integration points per element, each one is assigned with a copy of material model. If one records the stress using a command similar to plainrecorder 1 Element S 1, the request will be forwarded to the material models of all four integration points. Each point returns a vector of size 3, \(\begin{bmatrix}\sigma_{11}&\sigma_{22}&\sigma_{12}\end{bmatrix}\), four of those vectors will be concatenated so that the final record in the file will be a row of size 12.

time	IP1	IP1	IP1	IP2	IP2	IP2	IP3	IP3	IP3	IP4	IP4	IP4
time	\(\sigma_{11}\)	\(\sigma_{22}\)	\(\sigma_{12}\)	\(\sigma_{11}\)	\(\sigma_{22}\)	\(\sigma_{12}\)	\(\sigma_{11}\)	\(\sigma_{22}\)	\(\sigma_{12}\)	\(\sigma_{11}\)	\(\sigma_{22}\)	\(\sigma_{12}\)

The detailed quadrature schemes for elements are not well documented for the moment. The most used ones are Gauss and Lobatto with various orders.

Implementation Details

Creation

The creation of any elements does not validate anything beyond the scope of the element. For example, if the correct syntax appears to be the following.

element MyEle (1) (2) (3) (4)
# (1) int, unique tag
# (2) int, tag of the first node
# (3) int, tag of the second node
# (4) int, tag of the material

Then element MyEle 7 8 9 10 will create an element with tag 7, nodes 8, 9 and material 10, while element MyEle 7 8 9 or element MyEle 7 8 9 unexpected_str will fail the creation. Whether nodes 8, 9 and material 10 exist or not is not validated. Instead, these type of validations are performed during the initialisation stage, before the analysis stage. This means, the order of defining basic components is not important. It is valid to define an element before defining its connected nodes.

Initialisation

Before performing the analysis, all defined elements will be initialised. During this stage, each element will check the connected nodes and make sure they are active, and are able to accommodate the DoFs needed by the element. Local copies of the attached material models will be retrieved from the global storage. If any mismatch is found, for example, a uniaxial material model is assigned to a 3D element, the element will be disabled.

Analysis

During the analysis stage, the global solving algorithm solves the global system and updates nodal displacement accordingly. The new nodal displacement will be dispatched to all active elements for further analysis.

From the element's perspective, it is in charge of returning elemental nodal force vector based on given nodal displacement vector.

Interaction

The problem domain holds all necessary information for elements to update themselves. Elements do not directly interacts with global data storage. Rather, them only communicates with the associated nodes and sections/materials.

A complete interaction graph can be seen as follows. For elements themselves, apart from the connected nodes, they do not share information with any other objects by any means. Some elements may do not even need sections and/or materials.

graph LR
  A[Domain] -->|update_trial_status| B[Element];
  A -->|updaye_trial_status| J[Node];
  J -->|get_trial_displacement| B;
  B -->|update_trial_status| D[Section];
  D -->|update_trial_status| F[Material];
  F -->|get_trial_stress| D;
  F -->|get_trial_stiffness| D;
  D -->|get_trial_resistance| B;
  D -->|get_trial_stiffness| B;
  B -->|get_trial_resistance| A;
  B -->|get_trial_stiffness| A;